You are here:
  1. / iCalculator
  2. / Magnetism
  3. / Alternating Current Lc Circuits
  4. / Mechanical

Menu

Physics Lesson 16.14.2 - Electrical to Mechanical Analogy between Two Oscillating Systems

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

★★★★★ [ 1 Votes ]

Welcome to our Physics lesson on Electrical to Mechanical Analogy between Two Oscillating Systems, this is the second lesson of our suite of physics lessons covering the topic of Alternating Current. LC Circuits, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Electrical to Mechanical Analogy between Two Oscillating Systems

As stated earlier, an oscillating block and spring system represents a good analogy when trying to understand the behavior of quantities involved in a LC circuit, as both systems oscillate in a sinusoidal fashion. Thus, there are two types of energy involved in the block and spring system: one is kinetic (due to the block movement) and the other is (elastic) potential (stored in the spring). Neglecting the friction in the block and spring system and resistance in the LC circuit, we have

Etot = KEblock + EPEspring

for the block and spring system and

Wtot = Wcapacitor + Winductor

for the LC circuit. The following table makes this point clearer.

Physics Tutorials: This image provides visual information for the physics tutorial Alternating Current. LC Circuits

From the above table, it is easy to deduce the following correspondences:

x ⇢ Q
k ⇢ 1/C
v ⇢ i
m ⇢ L

In Section 11 (more precisely in tutorial 11.2 "Energy in Simple Harmonic Motion"), we have seen that the general equation for the angular frequency ω of a SHM is

ω = 2π/T

where T is the period of oscillation (i.e. the time needed to complete one oscillation). When applied for the mass and spring system, the equation of angular frequency becomes

ω = √k/m

where k is the spring constant and m is the mass of the attached object.

Substituting 1/C for k and L for m, we obtain for the angular frequency of a LC circuit:

ω = √1/C/L
= √1/L ∙ C
= 1/√L ∙ C

Giving that

ω = 2π ∙ f

where f is the frequency of oscillations in Hertz, we obtain for the frequency of oscillations in a RL circuit (electrical frequency):

2π ∙ f = 1/√L ∙ C

or

f = 1/2π ∙ √L ∙ C

The value of electrical frequency in US, Canada, Brazil, Colombia, some regions in Japan and some small countries in Central America is 60Hz, while in the rest of the world, this frequency is 50 Hz. This means the current makes 50 or 60 complete cycles in one second when flowing through an AC circuit.

Example 2

A LC circuit is operating somewhere in Europe. What is the capacitance of the capacitor if the inductance of the solenoid is 0.4 H?

Physics Tutorials: This image provides visual information for the physics tutorial Alternating Current. LC Circuits

Solution 2

Since the circuit is operating in Europe, the frequency of electricity must be 50 Hz. Therefore, giving that

f = 1/2π ∙ √L ∙ C

we obtain for the capacitance C after raising both parts of the equation in power two to remove the root:

f2 = 1/4π2 ∙ L ∙ C
C = 1/4π2 ∙ f2 ∙ L
= 1/4 ∙ 3.14 ∙ (50 Hz)2 ∙ (0.4 H)
= 7.96 × 10-5 F
= 79.6 μF

You have reached the end of Physics lesson 16.14.2 Electrical to Mechanical Analogy between Two Oscillating Systems. There are 5 lessons in this physics tutorial covering Alternating Current. LC Circuits, you can access all the lessons from this tutorial below.

More Alternating Current. LC Circuits Lessons and Learning Resources

Magnetism Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
16.14Alternating Current. LC Circuits
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
16.14.1LC Oscillations
16.14.2Electrical to Mechanical Analogy between Two Oscillating Systems
16.14.3LC Oscillations - A Quantitative Approach
16.14.4Angular Frequency
16.14.5Potential Difference in a LC Circuit

Whats next?

Enjoy the "Electrical to Mechanical Analogy between Two Oscillating Systems" physics lesson? People who liked the "Alternating Current. LC Circuits lesson found the following resources useful:

  1. Mechanical Feedback. Helps other - Leave a rating for this mechanical (see below)
  2. Magnetism Physics tutorial: Alternating Current. LC Circuits. Read the Alternating Current. LC Circuits physics tutorial and build your physics knowledge of Magnetism
  3. Magnetism Revision Notes: Alternating Current. LC Circuits. Print the notes so you can revise the key points covered in the physics tutorial for Alternating Current. LC Circuits
  4. Magnetism Practice Questions: Alternating Current. LC Circuits. Test and improve your knowledge of Alternating Current. LC Circuits with example questins and answers
  5. Check your calculations for Magnetism questions with our excellent Magnetism calculators which contain full equations and calculations clearly displayed line by line. See the Magnetism Calculators by iCalculator™ below.
  6. Continuing learning magnetism - read our next physics tutorial: Introduction to RLC Circuits

Help others Learning Physics just like you

Please provide a rating, it takes seconds and helps us to keep this resource free for all to use

★★★★★ [ 1 Votes ]

We hope you found this Physics lesson "Alternating Current. LC Circuits" useful. If you did it would be great if you could spare the time to rate this physics lesson (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.

Magnetism Calculators by iCalculator™

© iCalculator™ 2009 - 2024 | Physics Calculators | Privacy Policy | Terms of Use | Contact